A Phenomenological Model Where Vacuum Energy Tracks Local Proper Time Rate — Core Equation ρ_vac(x) = ρ₀ [1 + k (Φ(x)/c²)] — Implications for Evolving Dark Energy and a Null Test with Casimir Cavities (v0.2.2 explicit equation)

Phenomenological Model Where Vacuum Energy Tracks Local Proper Time Rate: Implications for Evolving Dark Energy and a Null Test with Casimir Cavities Core Equation:rho_vac(x) = rho_0 * [1 + k * (Phi(x) / c^2)] Abstract:We propose a phenomenological model where vacuum energy density tracks the local proper time rate (d_tau/dt ~ 1 + Phi/c^2). Phi is the local Newtonian potential (Phi=0 in void, Phi<0 in clusters). The motivation is twofold: (i) recent DESI hints that dark energy may be evolving, and (ii) the observed difference between the proper time rate in voids versus clusters. [1] If vacuum energy tracks proper time, voids (fast time, Phi~0) have slightly more vacuum energy than clusters (slow time, Phi<0) for k>0. Viewed from inside a cluster, this mimics evolving dark energy without a new fundamental field. BBN constrains the integrated effect to |epsilon| = |k * /c^2| < 4%. [1] The model predicts a concrete null test via annual modulation of Casimir pressure in the solar potential with a fractional amplitude of ~3.3e-10, testable with CANNEX data. Explicit Seasonal Prediction (for k>0): Jan 3 (Perihelion): Earth is deepest in the Sun's potential -> Proper time runs slowest -> Casimir Pressure Minimum (P_min) July 4 (Aphelion): Earth is farthest from the Sun -> Proper time runs fastest -> Casimir Pressure Maximum (P_max) Fractional Modulation: |Delta P| / P = |k| * (Delta Phi_sun / c^2) ~ |k| * 3.3e-10 [1, 2, 3] Draft v0.2.1 fixes the seasonal phasing sign from v0.2 to be consistent with "weaker where slower." This work is licensed under CC-BY 4. Draft v0.2.3 adds a short analysis of seasonal residuals in BIPM TAI clock data This supplementary note analyses seasonal residuals in BIPM TAI clock data (June/July vs Nov/Dec 2024) to check consistency with GR and with a phenomenological vacuum‑coupling model rho_vac = rho_0 (1 + k Phi / c^2). Two independent clocks (NPL 1412011 and PTB 1415245) show July running faster than December at the 1e-14 level, matching the expected GR seasonal sign and the predicted direction for k>0. The magnitude is strongly suppressed because TAI removes the solar redshift and applies steering, so these data cannot constrain k. The results do not contradict the vacuum‑coupling hypothesis. A decisive test remains a Casimir‑pressure comparison (CANNEX), where the predicted modulation is DeltaP/P = k * 3.3e-10 with January minimum and July maximum.